where \(k\in \lbrace \mathrm {x,y,z}\rbrace \) .
Note that the TVADCTA channels belong to the sub-family of Pauli channels known as depolarizing channels, since the additional symplectic twirl performed on the Pauli twirl in order to obtain the Clifford twirl symmetrizes the error distribution, which results in \(p_\mathrm {x}=p_\mathrm {y}=p_\mathrm {z}\)  [1]}, [2]}.
